Important Terms with Examples on Constructions

(i) A graduated scale, on one side of which centimetres and millimetres are marked off and on the other side inches and their parts are marked off.

(ii) A pair of set – squares, one with angles 90°, 60° and 30° and other with angles 90°, 45° and 45°.

(iii) A pair of dividers (or a divider) with adjustments.

(iv) A pair of compasses (or a compass) with provision of fitting a pencil at one end.

(v) A protractor.

In this chapter, you will do the following constructions using a ruler and a compass:

To bisect a given angle. For example: Construct an angle of 45 and hence construct 22 1/2.

To draw the perpendicular bisector of a given line segment. For example: Draw a line segment 6.4 cm and construct its perpendicular bisector.

To construct an angle of 60° etc. For example: Construct an angle of 120 and bisect it.

To construct a triangle given its base, a base angle and the sum of the other two sides. For example: Construct a right angled triangle whose hypotenuse measure 5.3 cm and the length of one of whose sides containing the right angle measures 4.5 cm.

To construct a triangle given its base, a base angle and the difference of the other two sides. For example: Construct a triangle ABC, in which BC = 5.2 cm and angle B = 30 and the difference of the other two sides is 3.5 cm.

To construct a triangle given its perimeter and its two base angles. For example: Construct a triangle, if the perimeter is 10.4 cm and the two base angles are 45 and 120.